Shear
Chapter 6: Geometric Transformation and Eigen Decomposition — Shear
From the book
Chapter 6: Geometric Transformation and Eigen Decomposition. In the chapter mind map this icon labels Shear. The discussion below is excerpted and lightly edited from § Shear in Mathematics for AI and Machine Learning.
In 2D, a shear transformation preserves one coordinate while shifting the other proportionally.
As shown in the book figure a 2D shear transformation tilts the object. Horizontal shear (red dashed line) shifts the top of the square, while vertical shear (green dash-dot line) shifts its side. Interestingly, shear transformations are area-preserving ($\det(H)=1$).
What this drawing shows
What you see. Shows a fixed black reference square with red (horizontal) and green (vertical) copies shearing slowly from the identity to factors $0.5$ and $0.8$, matching the chapter shear figure.
In the mind map. Chapter 6 — Shear. See From the book above for definitions, figures, and worked examples.
Where to read next
Read the full definitions, figures, and worked examples in Chapter 6: Geometric Transformation and Eigen Decomposition — see the mind-map node Shear.
